Anomalous Higgs oscillations mediated by Berry curvature and quantum metric

TL;DR

This paper reveals how Berry curvature and quantum metric influence Higgs mode generation in superconductors, enabling new detection methods and predicting second harmonic generation, with applications demonstrated in flat band systems like twisted bilayer graphene.

Contribution

It introduces the role of Berry curvature and quantum metric in Higgs mode generation, including linear coupling to electromagnetic fields and second harmonic generation, expanding understanding of superconducting Higgs dynamics.

Findings

Berry curvature and quantum metric enable Higgs detection even with vanishing band curvature.

Higgs mode can couple linearly to electromagnetic fields via Berry connection.

Prediction of second harmonic generation in superconductors due to geometric effects.

Abstract

Higgs spectroscopy, the study of Higgs bosons of a superconductor, is an emerging field in studying superconductivity. Here we show that the Berry curvature and the quantum metric of bands play a central role in the Higgs mode generation. They allow the detection of Higgs bosons even when the conventional contribution from the band curvature vanishes. Furthermore, we show that the Higgs mode can couple to the external electromagnetic field linearly when mediated by the Berry connection. As a result, we predict the existence of a second harmonic generation, in addition to the well-known third harmonic generation. We elucidate our theory further by considering a flat band superconductor realized by the Harper-Hubbard model and show that the geometric Higgs mode is lower bounded by the band Chern number. We demonstrate in twisted bilayer graphene the existence of the geometrically induced Higgs modes when superconductivity is realized in the nearly flat band at the magic angle.